A q-analogue of distance matrix of block graphs

Abstract

A q-analogue of the distance matrix (called q-distance matrix) of graphs, defined by Yan and Yeh (2007) [19], is revisited, which is formed from the distance matrix by replacing each nonzero entry α by 1+q+…+qα−1 (which would be reduced to α by setting q=1). This concept was also proposed by Bapat et al. (2006) [3]. A graph is called a block graph if every block is a clique (not necessarily of the same order). In this paper, the formula for the inverse of q-distance matrix of block graphs is presented, which generalizes some classical results about the inverse of distance matrix.